Magnetic instabilities along the superconducting phase boundary of Nb ∕ Ni multilayers Amish G. Joshi, Sergiy A. Kryukov, Lance E. De Long, Elvira M. Gonzalez, Elena Navarro, Javier E. Villegas, and Jose L. Vicent Citation: Journal of Applied Physics 101, 09G117 (2007); doi: 10.1063/1.2714302 View online: http://dx.doi.org/10.1063/1.2714302 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/101/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Probing the magnetization inside a superconducting Nb film by nuclear resonant scattering Appl. Phys. Lett. 99, 092508 (2011); 10.1063/1.3625941 Full spin switch effect for the superconducting current in a superconductor/ferromagnet thin film heterostructure Appl. Phys. Lett. 97, 102505 (2010); 10.1063/1.3486687 Magnetism and superconductivity in the superconductor/quasimagnet/ferromagnet Nb ∕ Pd ∕ Fe system J. Appl. 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Joshi,a� Sergiy A. Kryukov, and Lance E. De Longb� Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055 Elvira M. Gonzalez, Elena Navarro, Javier E. Villegas, and Jose L. Vicent Departamento de Fisica de Materiales, C. C. Fisicas, Universidad Complutense, 28040 Madrid, Spain �Presented on 9 January 2007; received 31 October 2006; accepted 23 January 2007; published online 8 May 2007� We report vibrating reed and superconducting quantum interference device magnetometer data that exhibit prominent dips or oscillations of the superconducting �SC� onset temperature, �TC�H� � 0.01 – 0.7 K, for a �Nb�23 nm� / Ni�5 nm��5 multilayer �ML� in dc magnetic fields applied nearly parallel to the ML plane. The vibrating reed data exhibit reproducible structures below TC that may reflect multiple SC transitions, but they are sensitive to ac field amplitude and dc field orientation. This striking behavior poses challenges for theoretical and experimental investigations of interfaces between SC and ferromagnetic layers that involve magnetic pair breaking effects, “pi phase shifts” of the SC order parameter, and exotic �“LOFF”� pairing states. Alternatively, the anomalies may mark dynamical instabilities within a confined, strongly anisotropic Abrikosov vortex lattice. © 2007 American Institute of Physics. �DOI: 10.1063/1.2714302� Multilayers �MLs� composed of alternating supercon- ducting �SC� and ferromagnetic �FM� thin films exhibit re- markable properties related to the destabilizing effect of magnetic interactions on SC pairing.1,2 This work was moti- vated by evidence of oscillations of TC�y� of order of 0.1 K for �Nb�23 nm� / Ni�y��5 ML �Nb layer thickness x = 23 nm and Ni layer thickness 2.5 � y � 6.0 nm�.3,4 Similar non- monotonic decreases of TC with FM layer thickness have been observed in other SC/FM bilayer, trilayer, and ML sys- tems, and attributed to a magnetic exchange coupling be- tween FM layers that oscillates in magnitude and sign as a function of the FM layer thickness.1,5–8 The SC proximity effect and magnetic pair breaking interactions within the Ni layers alter the magnitude and phase of the complex SC or- der parameter that determines the stability of the SC state of the ML, and may even induce “pi phase shifts” that can completely suppress superconductivity.8 A recent letter9 has reported the resistively measured TC of Ni�7 nm� / Nb�x� / Ni�7 nm� trilayers �16 nm � x � 52 nm� as a function of applied magnetic field that controls the relative orientation of the magnetizations of the two Ni lay- ers. Although very small, the observed shifts �2 � �TC � 41 mK� between parallel and antiparallel Ni layer orienta- tions were ten times larger than predicted by existing theo- ries for FM/SC/FM trilayers, using measured normal state parameters.10 We wish to point out that interpreting such shifts �TC � 10 mK is problematic because the experimental definition of TC�H� is not precise in applied magnetic fields that couple the equilibrium of the SC state to the weak stability of the Abrikosov vortex lattice. Indeed, modest probe currents can initiate dissipative motion or nonlinear dynamics of vortices11,12 in materials with few defects to “pin” them against Lorentz forces. Consequently, resistive determina- tions of TC�H� require an arbitrary “voltage criterion” that defines when dissipation due to vortex motion under the ap- plied current drive has dropped to negligible levels.9 The temperature interval between the initial decrease of resis- tance and apparent TC defined by the voltage criterion can be substantial and very sensitive to the probe current amplitude,13 and inferred TC’s do not necessarily reflect the equilibrium phase boundary between normal and SC states. On the other hand, shifts of order 10 mK are known to result from confinement of supercurrents and quantized mag- netic flux by mesoscopic boundaries such as thin-film cross sections4,14 or submicron holes lithographically patterned in SC films.11,15 In these cases, the TC shifts reflect an equilib- rium phase boundary when carefully measured at “vanish- ing” drive current.15,16 Magnetometry techniques offer alternative definitions of the SC onset, such as an initial diamagnetic change of the real part �m�� or an abrupt increase in the dissipative imagi- nary part �m�� of the ac magnetic moment in field-cooling �FC� experiments.11 Vibrating reed �VR� magnetometry is particularly well suited for measurements of thin-film or an- isotropic samples17 and is essentially a transverse ac suscep- tibility technique that employs very low ac fields generated perpendicular to the dc applied field.18,19 The high sensitivity of the VR to the entire sample bulk �which is not necessarily the case with resistivity measurements� at relatively low ac drives has been exploited to detect subtle transitions between equilibrium vortex lattice phases in bulk FM super- conductors17 and the onsets of plastic deformation and flow of the vortex lattice.12 a�Present address: National Physical Laboratory, Dr. K. S. Krishnan Road, New Delhi 110 012, India b�Author to whom correspondence should be addressed; electronic mail: delong@pa.uky.edu JOURNAL OF APPLIED PHYSICS 101, 09G117 �2007� 0021-8979/2007/101�9�/09G117/3/$23.00 © 2007 American Institute of Physics101, 09G117-1 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 147.96.14.15 On: Fri, 11 Sep 2015 17:27:27 http://dx.doi.org/10.1063/1.2714302 http://dx.doi.org/10.1063/1.2714302 http://dx.doi.org/10.1063/1.2714302 The �Nb�23 nm� / Ni�5 nm��5 ML was fabricated by dc magnetron sputtering on a Si �100� substrate and exhibited textured growth of Nb �110� and Ni �111� layers3,4 with only small Nb–Ni interdiffusion and interface roughness. In order to carry out vibrating reed experiments, a sample ML was glued onto one end of a rectangular reed �2.5 � 7 � 0.05 mm3, cut from a Si�100� wafer�, the opposite end of which was mounted onto one side of a piezoelectric transducer to form a cantilever beam arrangement.17 The transducer was driven by a synthesizer tuned to the funda- mental cantilever mode �frequency f = 650 – 865 Hz�, and the reed amplitude was detected capacitively using a resonant rf �327 MHz� cavity technique.17,20 The Si reed was oriented with its long dimension and the ML plane parallel to the dc magnetic field, which results in a transverse ac field �viewed in the moving VR frame� oriented perpendicular to the ap- plied dc field.18,19 Shifts of the VR frequency f �comparable to transverse m�� measure a magnetic restoring torque ex- erted on supercurrents that screen the ac field. The inverse VR amplitude A−1 measures ac losses �comparable to trans- verse m�� generated primarily by vortex motion.18 In order to complement the transverse VR response per- pendicular to the applied dc field, we also carried out con- ventional longitudinal measurements �with both dc and ac fields applied along the ML plane� using a Quantum Design MPMS5 supreconducting quantum interference device �SQUID� magnetometer operated at frequencies 0.1 � f � 10 Hz and drive amplitudes 0.01 � �oho � 0.3 mT. The real part �m�� of the ac moment measures the supercurrent �circulating perpendicular to the dc field� that screens the ac field, and the imaginary part �m�� mainly measures ac losses generated by SC vortex motion.18 We determined the SC onset temperatures using either the VR frequency f or amplitude A for a �Nb�23 nm� / Ni�5 nm��5 ML sample in parallel dc fields �see Fig. 1�. The data define two reversible phase boundaries that coincide remarkably well, except where they exhibit large downshifts at 0.22, 0.36, and 0.62 T �and smaller shifts at 0.1 and 0.58 T�, as shown in Fig. 2. Additional peaks or abrupt slope changes in f �T� and A�T� were also identified well below the upper SC onset �see Fig. 1� and were gener- ally found �almost independent of dc field� near characteris- tic temperatures of 5.1, 5.6, and 6.0 K. These anomalies could be grouped into two other trajectories that closely par- alleled the behavior of the SC onsets, as shown in Fig. 2. The complementary m��H , T� boundary determined from longitudinal SQUID data for field parallel to the ML plane exhibits strong oscillations �60 – 180 mK�, and these anoma- lies persist to fields of at least 0.65 T with an average period �o�H � 80 mT, as shown in Fig. 3. Additional SQUID mea- surements using ac field amplitudes �oho = 0.02, 0.05, 0.1, and 0.2 mT yield different trajectories—probably a result of FIG. 1. �Color online� VR frequency f and amplitude A vs temperature T for a �Nb�23 nm� / Ni�5 nm��5 ML in parallel magnetic field �oH = 0.12 T with VR drive V = 100 mV. Open symbols denote initial field-cooled �FC� data, and solid symbols denote subsequent FC-warming cycle �FCW� data. Red lines indicate the assumed normal-state base lines in f �T� and A�T�, and vertical arrows denote the temperatures of the SC onset near 6.6 K, and slope changes apparent near 6.0 and 5.6 K. FIG. 2. Magnetic field �H�-temperature �T� “phase boundary” between the SC and normal states for a �Nb�23 nm� / Ni�5 nm��5 ML, defined by an abrupt decrease in the VR amplitude A �open circles�. Data were taken in field-cooled-warming �FCW� experiments with VR drive V = 100 mV and dc field H nearly parallel to the ML plane. The left �open triangles� and middle �solid squares� trajectories mark temperatures of two anomalies in the slope of A�T� �see Fig. 1�. Solid lines are guides to the eye, and error bars denote uncertainties in extracting the points from data. Dashed lines denote possible phase transition lines between SC states of the entire ML or SC transitions within individual Nb layers. FIG. 3. �Color online� Magnetic field �H�-temperature �T� “phase bound- ary” between the SC and normal states for a �Nb�23 nm� / Ni�5 nm��5 ML, determined from SQUID magnetometer experiments at ac frequency f = 10 Hz and amplitude �oho = 0.2 mT, with applied dc field H parallel to the ML plane. Solid symbols denote the SC onset temperature indicated by an abrupt increase in the imaginary part m�, and open symbols by an abrupt diamagnetic shift in the real part m�, of the ac magnetic moment during FC. The divergence of the m� and m� data near �oH = 0.2 T reflects the onset of vortex depinning with increasing dc field. 09G117-2 Joshi et al. J. Appl. Phys. 101, 09G117 �2007� [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 147.96.14.15 On: Fri, 11 Sep 2015 17:27:27 vortex depinning and nonequilibrium disorder of the vortex lattice. Nevertheless, these data consistently exhibit oscilla- tions with the same average spacing and magnitudes shown in Fig. 3. Small oscillations �of order of 10 – 30 mK and rough pe- riod of 70 mT� were previously observed in lower-precision SQUID measurements4 on Nb / Ni ML. These variations were interpreted as “matching anomalies” at applied fields where the vortex density is equal to an integral multiple of the average density of strong vortex pinning centers.4,15 Match- ing anomalies are most prominent if pinning centers have a characteristic size ��T� � D � ��T� and are located on a peri- odic lattice.21 The SC/FM ML is essentially a one- dimensional periodic array of thin SC slabs spaced by Ni layers that strongly confine vortices when their planar cross sections are oriented perpendicular to an applied dc magnetic field H. A related matching effect has been predicted22 and observed in ML �Ref. 23� when NL vortices enter in succes- sive chains aligned parallel to the ML and H �an average oscillation period of 70 mT implies4 NL � 2 � 10 3�. More- over, calculations22,24,25 predict that a succession of vortex lattices will form within a thin SC slab in an increasing par- allel field, and these phases will have different packing to- pologies whose ranges of stability may not be strictly peri- odic in applied field. However, matching analyses of parallel dc field data �Fig. 3� do not clearly discriminate between cases for which there is either a nonzero SC order parameter within the Ni layers or isolated SC Nb layers �having distinct TC’s� sepa- rated by Ni layers having zero SC order parameter.4 Additional VR data were acquired at piezoelectric drives of 5, 10, 26, and 50 mV at selected dc fields of 0.08, 0.10, 0.36, and 0.62 T, at which thermal hysteresis was observed. The SC onsets exhibited extraordinary downshifts of 0.5 – 1.0 K with increasing VR drive, indicating weak vortex pinning and nonequilibrium vortex lattice disorder. The line of onsets near 6.5 K was found to extend to at least 0.62 T for drives of 5 – 26 mV, but disappeared at �oH � 0.2 T for drives V 50 mV, whereas a line of anomalies near 6.0 K was found to terminate at 0.62 T for V 26 mV �see Fig. 2�. The downshift of the SC onset near 0.2 T �0.62 T� therefore marks a hysteretic jump from the 6.5 to 6.0 K �6.0 – 5.5 K� “transition line,” possibly due to an increase in SC currents that drive the vortex lattice and have the potential �for criti- cal current densities JC � 10 7 A / cm2� to switch the magneti- zation direction of Ni domains. Both VR and ac SQUID magnetometry sensitively probe the pinning and dynamics of Abrikosov vortices,18 and the anomalies of Figs. 1–3 are clearly affected by vortex dynam- ics, but since the local vortex pinning force is proportional to the spatial gradient of the squared sc order parameter, the anomalies nevertheless reflect unusually strong variations in the stability of the sc state. Since both the real and imaginary parts of the VR signal behave similarly, the anomalies of Fig. 2 may well reflect SC phase transition lines for the entire ML or for individual Nb layers. The possibility remains open that they are caused by changes in the Ni-layer magnetizations that alter the phase and coupling between the SC order pa- rameter of adjacent Nb layers with applied dc field. Research at University of Kentucky supported by U.S. Department of Energy and Kentucky Science and Engineer- ing Foundation. Research at Universidad Complutense supported by Spanish Ministerio de Educacion y Ciencia, Comunidad de Madrid y Santander-UCM. One of the authors �A.G.J.� was supported by an Indian Department of Science and Technology BOYSCAST Fellowship No. SR/BY/P-01/ 04. 1B. Y. Jin and J. B. Ketterson, Adv. Phys. 38, 189 �1989�. 2M. B. Maple, Physica B 215, 110 �1995�. 3J. E. Villegas, E. Navarro, D. Jaque, E. M. Gonzalez, J. I. Martin, and J. L. Vicent, Physica C 369, 213 �2002�. 4L. E. 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Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 147.96.14.15 On: Fri, 11 Sep 2015 17:27:27